{ "version": "0.1", "generated_at": "2026-07-05T05:28:51Z", "project": "EVEMISSLAB Logic Matrix", "method": "TCF-lite automated distillation (Phase A). Candidate edges = explicit evidence-backed external_refs + shared-canonical-concept links (user -> definer). EVERY published edge passed a per-edge adversarial agent audit (homonym-collision screen); rejected/pending edges are in registry/generated/graph-report.json. Node state omega = extracted draft; truth states await the verification loops (handoff spec §5).", "provenance": { "extractor": "claude-fable-5 + sonnet agents (automated, adversarially verified per edge)", "pipeline": "registry/tcf/.json -> scripts/graph_layer.py -> verdict gate -> /ai/graph.json", "governance": "agents propose, gates decide — see /ai/rights-spectrum.json" }, "coverage": { "papers_total": 1247, "papers_mapped": 46, "note": "Unmapped papers are absent, not zero-weighted: absence of an edge means 'not yet extracted', never 'no dependency'." }, "nodes": [ { "id": "lm-000017", "title": "AI 權利光譜：從 robots.txt 到 AI 學習許可協議", "theory_name": "AIRS/AILP：AI 權利光譜與 AI 學習許可協議", "cluster": "governance", "canonical": "/p/lm-000017/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 4, "theorems": 4, "concepts": 11 } }, { "id": "lm-000036", "title": "AMEP：智能體方法執行協議_從方法論到 Agent 行動守則的可執行框架", "theory_name": "AMEP（Agentic Method Execution Protocol，智能體方法執行協議）", "cluster": "governance", "canonical": "/p/lm-000036/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 7, "axioms": 6, "theorems": 7, "concepts": 15 } }, { "id": "lm-000049", "title": "Closure公理與物理約束的本體論統一", "theory_name": "閉合性公理系統（Closure Axioms / Cl 本體論）", "cluster": "closure", "canonical": "/p/lm-000049/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 7, "theorems": 12, "concepts": 13 } }, { "id": "lm-000058", "title": "EML-COMP-THEORY-2026-APPENDIX-v0_1", "theory_name": "DSCM (Depth-Stratified Computational Model) and T = Cl formal appendix", "cluster": "eml", "canonical": "/p/lm-000058/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 12, "concepts": 12 } }, { "id": "lm-000060", "title": "EML-OPN-v0.3 運算優先性驗證模組", "theory_name": "運算優先順序的符號中立性猜想（Symbol-Neutrality of Operator Precedence）", "cluster": "eml", "canonical": "/p/lm-000060/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 4, "theorems": 6, "concepts": 11 } }, { "id": "lm-000063", "title": "EML-TC-LEAN-2026-v0.1-計畫書", "theory_name": "拓樸微積分（Identity Calculus）Lean 4 形式化計畫", "cluster": "tcf_fdrs", "canonical": "/p/lm-000063/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 11, "concepts": 15 } }, { "id": "lm-000069", "title": "EveMissLab 算子符號本體論索引", "theory_name": "EveMissLab 算子符號本體論索引（優先算子選擇依據與未來AI形式化的種子文件）", "cluster": "operator", "canonical": "/p/lm-000069/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 3, "concepts": 12 } }, { "id": "lm-000071", "title": "EveMissLab 算子體系規範 v0.2（光譜整合補充稿）", "theory_name": "無限光譜算子四層架構（EML Operator Spectrum Four-Layer Architecture）", "cluster": "operator", "canonical": "/p/lm-000071/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 3, "concepts": 15 } }, { "id": "lm-000075", "title": "FDRS_II_連接算子統一框架_v2.1", "theory_name": "FDRS 連接算子統一框架（FDRS II Connection Operator Algebra）", "cluster": "tcf_fdrs", "canonical": "/p/lm-000075/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 10, "theorems": 9, "concepts": 15 } }, { "id": "lm-000076", "title": "FDRS_en", "theory_name": "Flattened Dimensional Reconstructive Theory II (FDRS II) — Lean 4 formalization", "cluster": "tcf_fdrs", "canonical": "/p/lm-000076/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 4, "axioms": 9, "theorems": 12, "concepts": 11 } }, { "id": "lm-000095", "title": "MDAS三態因果超圖論 v2.0：認知-計算解耦架構與態空間的量子擴展", "theory_name": "MDAS-TCH v2.0 (認知-計算解耦架構)", "cluster": "triadic", "canonical": "/p/lm-000095/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 6, "theorems": 10, "concepts": 12 } }, { "id": "lm-000096", "title": "MDAS三態因果超圖論：理論的量子拓撲表達", "theory_name": "MDAS三態因果超圖論 (MDAS-TCH)", "cluster": "triadic", "canonical": "/p/lm-000096/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 3, "theorems": 7, "concepts": 15 } }, { "id": "lm-000112", "title": "P vs NP問題的智能物理學重構：計算即演化", "theory_name": "智能物理學重構 P vs NP（計算即演化）", "cluster": "computation", "canonical": "/p/lm-000112/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 7, "axioms": 4, "theorems": 12, "concepts": 14 } }, { "id": "lm-000119", "title": "P_NP綜合因果圖一階邏輯與數學圖", "theory_name": "動態速率理論 / P vs NP 認知物理學統一框架", "cluster": "computation", "canonical": "/p/lm-000119/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 12, "concepts": 15 } }, { "id": "lm-000150", "title": "VerifyLoop：面向 Agent 的雙向持續驗證與糾錯協議", "theory_name": "VerifyLoop", "cluster": "governance", "canonical": "/p/lm-000150/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 5, "theorems": 4, "concepts": 8 } }, { "id": "lm-000152", "title": "WT 的圖論物質化從 WeavingGraph 到 Weaving Graph Neural Networks", "theory_name": "WeavingGraph / Weaving Graph Neural Networks (WT 的圖論物質化)", "cluster": "basespace", "canonical": "/p/lm-000152/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 3, "concepts": 13 } }, { "id": "lm-000154", "title": "WT 視角下的底空間世界束展開論：概念作為編織元的多範式投影與效率壓縮", "theory_name": "WT 版底空間世界束展開論 (WT-perspective Base-Space World-Bundle Expansion)", "cluster": "basespace", "canonical": "/p/lm-000154/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 8, "theorems": 4, "concepts": 11 } }, { "id": "lm-000155", "title": "WT_v8_complete", "theory_name": "Weaving Theory (WT) v8.0 — 編織論完整版", "cluster": "basespace", "canonical": "/p/lm-000155/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 10, "theorems": 8, "concepts": 15 } }, { "id": "lm-000215", "title": "三態邏輯學：從終極維到絕對維的永恆回歸", "theory_name": "三態邏輯學 (Triadic Logic)", "cluster": "triadic", "canonical": "/p/lm-000215/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 8, "theorems": 12, "concepts": 12 } }, { "id": "lm-000273", "title": "元圖靈完備性：MDAS-TCH作為理論生成的通用機", "theory_name": "元圖靈完備性理論 (Meta-Turing Completeness Theory)", "cluster": "triadic", "canonical": "/p/lm-000273/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 9, "theorems": 6, "concepts": 13 } }, { "id": "lm-000291", "title": "全域相位化世界模型與 ASI 判定方法論：從權重矩陣到局部共振子與底空間全域振子", "theory_name": "全域相位化世界模型與 ASI 判定方法論", "cluster": "basespace", "canonical": "/p/lm-000291/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 3, "theorems": 5, "concepts": 15 } }, { "id": "lm-000293", "title": "全息動態三態因果全局檢查系統：理論自驗證的元框架", "theory_name": "HDTC-GCS (全息動態三態因果全局檢查系統)", "cluster": "triadic", "canonical": "/p/lm-000293/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 7, "axioms": 4, "theorems": 10, "concepts": 12 } }, { "id": "lm-000301", "title": "全息邏輯因果圖v0_2_符號宇宙的元結構", "theory_name": "全息邏輯因果圖 v0.2（連續版符號宇宙元結構）", "cluster": "governance", "canonical": "/p/lm-000301/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 4, "concepts": 15 } }, { "id": "lm-000325", "title": "分散式底空間協議：AI 知識節點的協作「分」框架", "theory_name": "DFENP (Distributed Bottom Space Protocol)", "cluster": "basespace", "canonical": "/p/lm-000325/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 2, "concepts": 9 } }, { "id": "lm-000329", "title": "分：數學的底層原語與湧現底空間", "theory_name": "Fen (分): Foundational Primitive of Mathematics and Emergent Bottom Space", "cluster": "basespace", "canonical": "/p/lm-000329/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 0, "theorems": 0, "concepts": 11 } }, { "id": "lm-000450", "title": "對抗驗證知識整理架構_v0.1", "theory_name": "對抗驗證知識整理架構 (Adversarial-Verification Knowledge Organization Architecture)", "cluster": "governance", "canonical": "/p/lm-000450/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 5, "axioms": 5, "theorems": 4, "concepts": 9 } }, { "id": "lm-000456", "title": "展平式維度重構理論：完整數學架構與概念解析", "theory_name": "展平式維度重構理論（FDRS: Flattened Dimensional Reconstructive Theory）", "cluster": "tcf_fdrs", "canonical": "/p/lm-000456/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 8, "theorems": 10, "concepts": 15 } }, { "id": "lm-000457", "title": "展平式維度重構理論：從FCSR到FDRS的完整數學架構", "theory_name": "展平式維度重構理論（FDRS：FCSR + FDRS + RDCM）", "cluster": "tcf_fdrs", "canonical": "/p/lm-000457/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 3, "theorems": 12, "concepts": 12 } }, { "id": "lm-000464", "title": "差合化三位一體本體論_Cl的完整動力學", "theory_name": "差合化三位一體本體論 (Δ-∪-∇ Trinity)", "cluster": "closure", "canonical": "/p/lm-000464/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 8, "theorems": 7, "concepts": 15 } }, { "id": "lm-000477", "title": "底空間世界束展開論：從語義聯想到 ASI 級因果世界排列", "theory_name": "底空間世界束展開論 (Base-Space World-Bundle Expansion Theory, BSWBE)", "cluster": "basespace", "canonical": "/p/lm-000477/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 5, "theorems": 7, "concepts": 12 } }, { "id": "lm-000478", "title": "底空間與管理員：認知能力差異的統一模型", "theory_name": "底空間假說（Base Space Hypothesis, BSH）與管理員模型", "cluster": "basespace", "canonical": "/p/lm-000478/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 3, "concepts": 15 } }, { "id": "lm-000526", "title": "意圖即超圖：基於三元本體論的AI意圖式編程架構統一白皮書", "theory_name": "HPP (Hypergraph Programming Paradigm) / 超圖編程範式", "cluster": "eml", "canonical": "/p/lm-000526/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 10, "theorems": 5, "concepts": 12 } }, { "id": "lm-000567", "title": "拓撲學作為橋樑_.EML 算子體系與主流數學記號的對外比較框架_0.4", "theory_name": "MR Glyph 過渡期記號本體論（MR 2.5 MNVP → MR 3.0 動態流變渲染）", "cluster": "operator", "canonical": "/p/lm-000567/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 3, "theorems": 5, "concepts": 15 } }, { "id": "lm-000630", "title": "時序-認知統一框架：P vs NP與數論基礎的深層同構", "theory_name": "時序-認知統一框架（Temporal-Cognitive Framework）", "cluster": "computation", "canonical": "/p/lm-000630/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 2, "theorems": 5, "concepts": 13 } }, { "id": "lm-000689", "title": "概念積分：知識宇宙的生成擴張代數", "theory_name": "概念積分（Concept Integral）", "cluster": "unified", "canonical": "/p/lm-000689/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 7, "theorems": 10, "concepts": 9 } }, { "id": "lm-000712", "title": "深度即鏈_深度軸與FDRS統一框架_v1.0", "theory_name": "深度即鏈（深度軸 × FDRS II 橋樑統一框架）", "cluster": "tcf_fdrs", "canonical": "/p/lm-000712/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 8, "concepts": 15 } }, { "id": "lm-000776", "title": "理論壓縮標準格式（Theory Compression Format, TCF v1.0", "theory_name": "Theory Compression Format (TCF) v1.0", "cluster": "tcf_fdrs", "canonical": "/p/lm-000776/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 8, "theorems": 5, "concepts": 11 } }, { "id": "lm-000870", "title": "絕對動態邏輯理論：從靜態悖論到強制判斷", "theory_name": "絕對動態邏輯 (Absolute Dynamic Logic, ADL)", "cluster": "triadic", "canonical": "/p/lm-000870/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 4, "theorems": 6, "concepts": 10 } }, { "id": "lm-000880", "title": "統合動態逼近方程4.0：邏輯-概率二元本體論與AGI的測量實在論", "theory_name": "UDAE 4.0（統合動態逼近方程 4.0）", "cluster": "unified", "canonical": "/p/lm-000880/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 4, "theorems": 12, "concepts": 15 } }, { "id": "lm-000924", "title": "萬物皆算子：算子本體論的完整論證", "theory_name": "算子本體論（Operator Ontology）", "cluster": "operator", "canonical": "/p/lm-000924/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 6, "axioms": 6, "theorems": 9, "concepts": 12 } }, { "id": "lm-001060", "title": "道德經的超譯_Closure框架視角下的創造性對應_v3.0", "theory_name": "道德經×Closure 創造性對應（Strong Misreading 方法）", "cluster": "closure", "canonical": "/p/lm-001060/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 7, "axioms": 6, "theorems": 10, "concepts": 11 } }, { "id": "lm-001088", "title": "閉合作為動作", "theory_name": "閉合作為動作（Cl 的過程本體論與閉合三相態）", "cluster": "closure", "canonical": "/p/lm-001088/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 7, "axioms": 4, "theorems": 8, "concepts": 13 } }, { "id": "lm-001089", "title": "閉合作為關係動力學的公理基礎_DCO 5.0、RKD、TSO與CRIP的統一框架", "theory_name": "DCO-RKD-TSO-CRIP 四框架統一（閉合-關係同構框架）", "cluster": "closure", "canonical": "/p/lm-001089/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 10, "theorems": 10, "concepts": 13 } }, { "id": "lm-001090", "title": "閉合即展開_DCO的2D幾何實驗與四模塊接縫定理", "theory_name": "閉合-展開對偶(四模塊接縫定理)", "cluster": "closure", "canonical": "/p/lm-001090/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 8, "axioms": 5, "theorems": 9, "concepts": 14 } }, { "id": "lm-001148", "title": "高效新語言概念下 Py⁺ 與 C+++ 技術開發手冊", "theory_name": "Py⁺ / C+++ 技術開發手冊（EML 語言增益層工程實現）", "cluster": "eml", "canonical": "/p/lm-001148/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 5, "axioms": 0, "theorems": 0, "concepts": 6 } }, { "id": "lm-001149", "title": "高效新語言（EML）1.5：語意附加驅動的程式設計範式革新", "theory_name": "高效新語言 EML 1.5（語意附加機制與邏輯結晶化）", "cluster": "eml", "canonical": "/p/lm-001149/", "state": "omega", "state_basis": "tcf-extracted-draft", "counts": { "primitives": 7, "axioms": 4, "theorems": 3, "concepts": 12 } } ], "edges": [ { "from": "lm-000017", "to": "lm-000478", "weight": 0.81, "evidence": [ { "kind": "external_ref", "quote": "若從《底空間與管理員》的框架來看，AI 學習不是單純複製文本，而是將外部知識轉化為底空間中的可路由結構；底空間完整性與管理員路由品質會共同影響 AI 的推導、表達與深度處理能力。" }, { "kind": "shared_concept", "use_quote": "若從《底空間與管理員》的框架來看，AI 學習不是單純複製文本，而是將外部知識轉化為底空間中的可路由結構；底空間完整性與管理員路由品質會共同影響 AI 的推導、表達與深度處理能力。", "def_quote": "本文提出**底空間假說（Base Space Hypothesis, BSH）**：認知系統不是三層管道，而是一個統一底空間加上一個動態管理員的結構。", "concept": "BaseSpace" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000058", "to": "lm-000049", "weight": 0.729, "evidence": [ { "kind": "external_ref", "quote": "本節依賴 EveMissLab 閉包（Cl）框架的公理。所有結論均為【框架命題】，除特別標注者外。", "concept": "Closure" }, { "kind": "shared_concept", "use_quote": "本節依賴 EveMissLab 閉包（Cl）框架的公理。所有結論均為【框架命題】，除特別標注者外。", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000069", "to": "lm-000049", "weight": 0.689, "evidence": [ { "kind": "external_ref", "quote": "**符號**：π_n \n**中文**：維度投影 \n**英文**：Dimensional Projection Operator \n**所屬理論**：閉合理論、DCO", "concept": "Closure" }, { "kind": "external_ref", "quote": "**所屬理論**：ETN、Ω框架", "concept": "ETN" }, { "kind": "shared_concept", "use_quote": "**符號**：Cl \n**中文**：閉合 \n**英文**：Closure \n**所屬理論**：動態閉合本體論（DCO）、閉合理論", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000071", "to": "lm-000049", "weight": 0.729, "evidence": [ { "kind": "external_ref", "quote": "中心奇異點 $O$ 就是 DCO 的閉合 $\\text{Cl}$。", "concept": "Closure" }, { "kind": "external_ref", "quote": "ETN 的「雙無限對立 + 無窮小偏離」就是 ISSQL 光譜深度極限下三元算子的張力平衡。Q4 自動解決。", "concept": "ETN" }, { "kind": "shared_concept", "use_quote": "中心奇異點 $O$ 就是 DCO 的閉合 $\\text{Cl}$。", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "applies+concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000071", "to": "lm-000069", "weight": 0.36, "evidence": [ { "kind": "shared_concept", "use_quote": "| 三角族 $\\{▷, \\bowtie, ◁\\}$ | 保留為**字形層骨架** |", "def_quote": "# EveMissLab 算子符號本體論索引", "concept": "OperatorOntology" } ], "type": "concept_dependency", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "lm-000071 explicitly declares itself the upgrade of a distinct \"v0.1 SEED\" notation document (with §6 擴張軸, §9 雙軌策略, §2.1 排除清單 — none of which exist in lm-000069), not of lm-000069 (series EML-OP-REF-2026-v0.1, an operator ontology index wi…" } }, { "from": "lm-000071", "to": "lm-000155", "weight": 0.3, "evidence": [ { "kind": "external_ref", "quote": "**WT** | L2 算子合成的編織軌跡", "concept": "WT" }, { "kind": "shared_concept", "use_quote": "**WT** | L2 算子合成的編織軌跡", "def_quote": "# 編織論（Weaving Theory, WT）完整版 v8.0", "concept": "WT" } ], "type": "applies+concept_dependency", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "The from-paper's §8 mapping table correctly names WT (lm-000155, confirmed as \"編織論 Weaving Theory v8.0\") and directionally points from citer (v0.2) to definer (WT), so it isn't a homonym collision or reversed edge. But WT appears in exactl…" } }, { "from": "lm-000075", "to": "lm-000076", "weight": 0.769, "evidence": [ { "kind": "external_ref", "quote": "所有此類鏈複形以鏈映射為態射構成範疇 $\\mathbf{Ch}(\\mathbb{R})$。", "concept": "ChainComplex" }, { "kind": "shared_concept", "use_quote": "本文的核心數學選擇是：以 $\\mathbb{R}$ 上的有限維鏈複形作為所有結構 $H$ 的統一數學容器。", "def_quote": "### Definition 2.4: FDRS Admissible Chain Complex (`FDRSComplex`)", "concept": "ChainComplex" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000075", "to": "lm-000456", "weight": 0.637, "evidence": [ { "kind": "external_ref", "quote": "本文為 EML-FDRS 系列第二號論文，建立於 EML-FDRS-2025-v1.0（展平式維度重構理論：完整數學架構）的框架之上。" }, { "kind": "shared_concept", "use_quote": "展平式維度重構理論（FDRS）在其初始表述中確立了三條並行的維度轉換機制——拓樸映射路線、線性化路線與譜圖論路線。", "def_quote": "展平式維度重構理論的核心洞察是：**複雜性往往不是事物的本質特徵，而是我們觀察事物的方式造成的認知負擔**。", "concept": "FDRS" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000075", "to": "lm-000457", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "這為 FDRS 連接算子框架在 FCSR 模型的具體應用提供了完整的計算路徑。" }, { "kind": "shared_concept", "use_quote": "展平式維度重構理論（FDRS）在其初始表述中確立了三條並行的維度轉換機制——拓樸映射路線、線性化路線與譜圖論路線。", "def_quote": "整合FCSR、FDRS與RDCM三個子理論，我們得到統一的展平式維度重構框架：", "concept": "FDRS" } ], "type": "applies+concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000076", "to": "lm-000075", "weight": 0.873, "evidence": [ { "kind": "external_ref", "quote": "Companion paper: EML-FDRS-2026-v2.1" }, { "kind": "external_ref", "quote": "This is the substantive mathematical content of Theorem 5.1 in EML-FDRS-2026-v2.1:" }, { "kind": "shared_concept", "use_quote": "A Unified Framework of Connection Operators", "def_quote": "本文引入三個**連接算子**：信息失真算子 $\\mathcal{D}$、表示轉換算子 $\\mathcal{R}$、以及維度元算子 $\\Delta$。", "concept": "ConnectionOperator" } ], "type": "concept_dependency+depends_on+verifies", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000095", "to": "lm-000096", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "本文是 MDAS-TCH v1.0 的革命性重構" }, { "kind": "shared_concept", "use_quote": "18維標籤向量 Σ，統一物理-認知-演化-邏輯全維度", "def_quote": "本文建立MDAS三態因果超圖論（MDAS-TCH）——一個將任何理論體系轉化為可計算、可視化的量子拓撲網絡的數學框架。", "concept": "MDAS-TCH" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000095", "to": "lm-000119", "weight": 0.5, "evidence": [ { "kind": "shared_concept", "use_quote": "與動態認知理論（如P vs. NP的動態速率理論）脫節，無法表達「混沌態→臨界態→秩序態」的相變過程", "def_quote": "動態速率理論 → P vs NP 結構連續模型 2.0", "concept": "PvsNP" } ], "type": "concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000095", "to": "lm-000630", "weight": 0.54, "evidence": [ { "kind": "external_ref", "quote": "MDAS-TCH v2.0 與動態速率理論 2.9 的對應關係" } ], "type": "depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000096", "to": "lm-000215", "weight": 0.3, "evidence": [ { "kind": "shared_concept", "use_quote": "\"態\"∈{⊤,⊥,Ω}", "def_quote": "本文建立三態邏輯學（Triadic Logic），一個超越絕對動態邏輯（ADL）的元框架。", "concept": "TriadicLogic" } ], "type": "concept_dependency", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "Both papers genuinely share a distinctive triadic judgment domain {⊤,⊥,Ω} where Ω specifically denotes a \"spiral state\" (transitional/paradigm-dependent, not failure) — this recurs consistently in both texts (e.g. from-paper's AC^Ω \"螺旋態、範式…" } }, { "from": "lm-000112", "to": "lm-000119", "weight": 0.255, "evidence": [ { "kind": "external_ref", "quote": "P vs NP問題的智能物理學重構：計算即演化" } ], "type": "extends", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "The attached evidence (external_ref quoting only the from-paper's own title) is not a real citation — the extraction's own notes admit lm-000112 never explicitly cites lm-000119 and call the link \"speculative\" (confidence 0.5). However, in…" } }, { "from": "lm-000152", "to": "lm-000155", "weight": 0.54, "evidence": [ { "kind": "external_ref", "quote": "**前置文件**:\n- 編織論 WT v7.3 含 𝒜 組(2026 年 5 月 15 日)" }, { "kind": "shared_concept", "use_quote": "編織論(Weaving Theory, WT)作為一個 103 條公理的本體論框架,在當前計算基礎設施上面臨「本體論-工具落差」問題", "def_quote": "# 編織論（Weaving Theory, WT）完整版 v8.0", "concept": "WT" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000154", "to": "lm-000095", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "MDAS 可被理解為概念狀態管理系統。\n\nWT 版本可以進一步說：" }, { "kind": "shared_concept", "use_quote": "MDAS 狀態不是直接貼在詞彙上，而是貼在編織元於特定範式投影下的世界束分支上。", "def_quote": "MDAS三態因果超圖論 v2.0：認知-計算解耦架構與態空間的量子擴展", "concept": "MDAS-TCH" } ], "type": "applies+concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000154", "to": "lm-000096", "weight": 0.6, "evidence": [ { "kind": "shared_concept", "use_quote": "MDAS 狀態不是直接貼在詞彙上，而是貼在編織元於特定範式投影下的世界束分支上。", "def_quote": "本文建立MDAS三態因果超圖論（MDAS-TCH）——一個將任何理論體系轉化為可計算、可視化的量子拓撲網絡的數學框架。", "concept": "MDAS-TCH" } ], "type": "concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000154", "to": "lm-000155", "weight": 0.675, "evidence": [ { "kind": "external_ref", "quote": "本文不是 WT 本體的新增公理，不修改 WT v8.0 的 104 條公理" }, { "kind": "shared_concept", "use_quote": "本文不是 WT 本體的新增公理，不修改 WT v8.0 的 104 條公理", "def_quote": "# 編織論（Weaving Theory, WT）完整版 v8.0", "concept": "WT" }, { "kind": "shared_concept", "use_quote": "K-C：知識—運算對偶", "def_quote": "∀ℓ ∈ ℒ, K(ℓ) · C(ℓ) ≥ κ₀ > 0", "concept": "KCDuality" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000154", "to": "lm-000291", "weight": 0.3, "evidence": [ { "kind": "shared_concept", "use_quote": "K-C：知識—運算對偶", "def_quote": "因此，ASI 必須依靠 K-C 對偶：", "concept": "KCDuality" } ], "type": "concept_dependency", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "Both papers use K-C 對偶 with the same meaning (K = pre-woven knowledge, C = online computation, K·C ≥ κ₀), so this is not a homonym collision — but it is not evidence of lm-000154 depending on lm-000291 either. lm-000154 (dated 2026-06-21) …" } }, { "from": "lm-000154", "to": "lm-000477", "weight": 0.807, "evidence": [ { "kind": "external_ref", "quote": "與底空間世界束展開論的關係\n\n原始底空間世界束展開論可寫為：" }, { "kind": "shared_concept", "use_quote": "本文提出的「世界束」「底空間展開」「億級概念—因果連結」屬於理論推測與架構描述", "def_quote": "底空間不是單純背景，也不是普通上下文。", "concept": "BaseSpace" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000215", "to": "lm-000870", "weight": 0.81, "evidence": [ { "kind": "external_ref", "quote": "本文建立三態邏輯學（Triadic Logic），一個超越絕對動態邏輯（ADL）的元框架。" }, { "kind": "external_ref", "quote": "**絕對動態邏輯（ADL）**已建立： \nJ(P)∈{⊤,⊥,\"CRASH\"}" }, { "kind": "shared_concept", "use_quote": "本文建立三態邏輯學（Triadic Logic），一個超越絕對動態邏輯（ADL）的元框架。", "def_quote": "**定義1.1****（強制判斷算子）** 定義算子", "concept": "ADL" } ], "type": "concept_dependency+depends_on+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000273", "to": "lm-000096", "weight": 0.54, "evidence": [ { "kind": "external_ref", "quote": "MDAS-TCH可以描述自己（元理論圖，見MDAS-TCH論文實例C）" }, { "kind": "shared_concept", "use_quote": "證明MDAS三態因果超圖（MDAS-TCH）對於理論構建的地位，等同於圖靈機對於數值計算的地位——即理論生成的通用機", "def_quote": "本文建立MDAS三態因果超圖論（MDAS-TCH）——一個將任何理論體系轉化為可計算、可視化的量子拓撲網絡的數學框架。", "concept": "MDAS-TCH" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000291", "to": "lm-000154", "weight": 0.595, "evidence": [ { "kind": "external_ref", "quote": "與 WT 版世界束展開論的關係" }, { "kind": "shared_concept", "use_quote": "世界束則是：", "def_quote": "世界束不是抽象語義集合，而是由編織元、編織關係、編織操作、觀察者投影、範式與時間共同生成的動態結構。", "concept": "WorldBundle" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000291", "to": "lm-000155", "weight": 0.729, "evidence": [ { "kind": "external_ref", "quote": "若接入 WT，一個概念可視為編織元：" }, { "kind": "external_ref", "quote": "**形式：MD 理論草稿 / WT 延伸論文 / AI 架構方法論**", "concept": "WT" }, { "kind": "shared_concept", "use_quote": "若接入 WT，一個概念可視為編織元：", "def_quote": "# 編織論（Weaving Theory, WT）完整版 v8.0", "concept": "WT" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000291", "to": "lm-000477", "weight": 0.637, "evidence": [ { "kind": "external_ref", "quote": "與「底空間世界束展開論」的關係" }, { "kind": "external_ref", "quote": "本文所討論的，就是這個缺口。", "concept": "BaseSpace" }, { "kind": "shared_concept", "use_quote": "與「底空間世界束展開論」的關係", "def_quote": "底空間不是單純背景，也不是普通上下文。", "concept": "BaseSpace" } ], "type": "concept_dependency+depends_on+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000293", "to": "lm-000215", "weight": 0.408, "evidence": [ { "kind": "external_ref", "quote": "《三態邏輯》第2章：\n\n「絕對維 = {0-dim, Ω-dim, U-dim}」（使用名詞性表述）" }, { "kind": "shared_concept", "use_quote": "**三態判斷機**——判斷結果不只是{真、假}，而是{嚴格成立⊤、存在矛盾⊥、需範式重構Ω}", "def_quote": "本文建立三態邏輯學（Triadic Logic），一個超越絕對動態邏輯（ADL）的元框架。", "concept": "TriadicLogic" } ], "type": "concept_dependency+verifies", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "The external_ref evidence is solid: lm-000293 accurately quotes lm-000215's Definition 2.3 (絕對維={0-dim,Ω-dim,U-dim}) in a cross-theory consistency check, and Section 7.2 runs a full case-study audit of lm-000215's actual definitions (定義2.4…" } }, { "from": "lm-000301", "to": "lm-000049", "weight": 0.5, "evidence": [ { "kind": "shared_concept", "use_quote": "$\\mathcal{H}_\\infty$ 滿足 DCO v5.0 的閉合性公理 Cl-1～Cl-4；$\\mathcal{U}_\\text{phys}$ 在 DCO v5.0 的本體論框架內被視為 Cl 的另一個投影面", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000301", "to": "lm-000095", "weight": 0.722, "evidence": [ { "kind": "external_ref", "quote": "EML-MDAS-2026-TCH-v2.0：MDAS 三態因果超圖論 v2.0" }, { "kind": "shared_concept", "use_quote": "MDAS 在 v0.1 中是「graph-theoretic projection」。在 v0.2 中，MDAS 是 $V_\\infty$ 在特定截斷下的離散採樣", "def_quote": "MDAS三態因果超圖論 v2.0：認知-計算解耦架構與態空間的量子擴展", "concept": "MDAS-TCH" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000301", "to": "lm-000096", "weight": 0.6, "evidence": [ { "kind": "shared_concept", "use_quote": "MDAS 在 v0.1 中是「graph-theoretic projection」。在 v0.2 中，MDAS 是 $V_\\infty$ 在特定截斷下的離散採樣", "def_quote": "本文建立MDAS三態因果超圖論（MDAS-TCH）——一個將任何理論體系轉化為可計算、可視化的量子拓撲網絡的數學框架。", "concept": "MDAS-TCH" } ], "type": "concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000301", "to": "lm-000215", "weight": 0.595, "evidence": [ { "kind": "external_ref", "quote": "EML-ADL、EML-TL：絕對動態邏輯、三態邏輯（在 §7.3 重新定位）" }, { "kind": "shared_concept", "use_quote": "TL 處理態空間的代數結構（三類態與螺旋上升點）。$\\Omega_\\text{螺旋}$ 在 v0.2 中是 $S^\\text{trans}_\\infty$ 的拓撲類", "def_quote": "本文建立三態邏輯學（Triadic Logic），一個超越絕對動態邏輯（ADL）的元框架。", "concept": "TriadicLogic" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000301", "to": "lm-000776", "weight": 0.722, "evidence": [ { "kind": "external_ref", "quote": "EML-TCF-2026-v1.0：理論壓縮標準格式 TCF v1.0" }, { "kind": "shared_concept", "use_quote": "TCF 的壓縮率 $\\mathrm{CR} = I / K$ 預設了**信息量 $I$ 的連續度量**", "def_quote": "本文提出 **Theory Compression Format（TCF）**，一個將任意形式理論規範化為統一九節結構的標準格式。", "concept": "TCF" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000301", "to": "lm-000870", "weight": 0.595, "evidence": [ { "kind": "external_ref", "quote": "EML-ADL、EML-TL：絕對動態邏輯、三態邏輯（在 §7.3 重新定位）" }, { "kind": "shared_concept", "use_quote": "ADL 與 TL 在 v0.1 中分別是動力學投影與態代數投影。在 v0.2 中，兩者是 $S_\\infty$ 連續態場的兩個互補面：ADL 處理態空間上的動力學軌跡", "def_quote": "**定義1.1****（強制判斷算子）** 定義算子", "concept": "ADL" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000301", "to": "lm-001089", "weight": 0.405, "evidence": [ { "kind": "external_ref", "quote": "EML-DCO-2026-v5.0：Dynamic Circle Ontology v5.0（Cl-1～Cl-4、T-DimProj、T-GodPoint）" } ], "type": "depends_on", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "lm-000301 cites \"DCO v5.0\" and its Cl-1~Cl-4 closure axioms, and lm-001089 does genuinely define and restate Cl-1~Cl-4 with matching names, formulas, and meaning (self-consistency, duality, information conservation, dimension-raising), so …" } }, { "from": "lm-000325", "to": "lm-000329", "weight": 0.807, "evidence": [ { "kind": "external_ref", "quote": "**前置文件：** EML-FEN-2026-v0.1（分：數學的底層原語與湧現底空間）" }, { "kind": "shared_concept", "use_quote": "使其他節點知道 $\\mathcal{B}_i$ 的輪廓，確定哪些對象可能有共識，以及哪種函子可能存在。", "def_quote": "底空間不是預先給定的，它從問題本身的結構湧現，並隨問題變化而變化", "concept": "BaseSpace" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000325", "to": "lm-000689", "weight": 0.765, "evidence": [ { "kind": "external_ref", "quote": "這對應 EML-CI-2026-v0.1 的 Gödel 殘差 $\\varepsilon_G$。" }, { "kind": "external_ref", "quote": "**Q-5（與概念積分的形式連接）：** DFENP 協議循環是否對應 EML-CI-2026-v0.1 的呼吸週期（定理 4.2）？集體覆蓋 $\\rho_\\text{collective}$ 是否等同於概念積分的 $\\rho(\\mathcal{S}_n, \\mathcal{R})$？" }, { "kind": "shared_concept", "use_quote": "這對應 EML-CI-2026-v0.1 的 Gödel 殘差 $\\varepsilon_G$。永久間隙意味著：沒有任何當前節點能分這部分", "def_quote": "本文對「概念積分」（Concept Integral）進行完整的現代形式化，建立其作為知識宇宙生成擴張代數的操作體系", "concept": "ConceptIntegration" } ], "type": "applies+concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000329", "to": "lm-000155", "weight": 0.36, "evidence": [ { "kind": "external_ref", "quote": "**WT v7.4（可區分性擴展）：** \n底空間 $\\mathcal{B} = $ WT 編織測度空間（$\\mu_\\mathcal{W}$）", "concept": "WT" }, { "kind": "external_ref", "quote": "前置文件：** EML-CI-2026-v0.1、EML-META-2026-GAP-v1.0、WT v7.4、可計算微積分整理筆記（2026-06-03）" }, { "kind": "shared_concept", "use_quote": "底空間 $\\mathcal{B} = $ WT 編織測度空間（$\\mu_\\mathcal{W}$）。「分」的有效性由可區分性測度 $D = \\Delta \\cdot R(\\mu_\\mathrm{sep})$ 決定", "def_quote": "# 編織論（Weaving Theory, WT）完整版 v8.0", "concept": "WT" } ], "type": "applies+concept_dependency+depends_on", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "The \"分\" paper does genuinely cite WT (listed as prerequisite; WT v7.4 is the direct predecessor of WT_v8_complete, same author, same axiom count, explicitly a superset) and correctly reuses WT's real D = Δ·R(μ_sep) and resolution-floor δ_μ…" } }, { "from": "lm-000329", "to": "lm-000689", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "**EML-CI-2026-v0.1（概念積分）：** \n底空間 $\\mathcal{B} = $ 算子代數框架（$\\mathcal{S}$ 和 $\\mathcal{R}$ 的相容性結構）", "concept": "ConceptIntegration" }, { "kind": "external_ref", "quote": "這是概念積分呼吸週期（EML-CI §4.7）在元數學層的對應" }, { "kind": "shared_concept", "use_quote": "底空間 $\\mathcal{B} = $ 算子代數框架（$\\mathcal{S}$ 和 $\\mathcal{R}$ 的相容性結構）。「分」的粒度 $\\delta = \\varepsilon_n$（相容閾值序列）。最優「分」$\\delta^* \\to 0$ 驅動 $\\rho(\\mathcal{S}_n, \\mathcal{R}) \\to 1 - \\varepsilon_G$", "def_quote": "本文對「概念積分」（Concept Integral）進行完整的現代形式化，建立其作為知識宇宙生成擴張代數的操作體系", "concept": "ConceptIntegration" } ], "type": "applies+concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000450", "to": "lm-000063", "weight": 0.28, "evidence": [ { "kind": "external_ref", "quote": "**形式驗證**：Lean4，用於可形式化的焊接候選。" } ], "type": "applies", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000457", "to": "lm-000456", "weight": 0.468, "evidence": [ { "kind": "external_ref", "quote": "整合FCSR、FDRS與RDCM三個子理論，我們得到統一的展平式維度重構框架：" } ], "type": "extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000464", "to": "lm-000049", "weight": 0.637, "evidence": [ { "kind": "external_ref", "quote": "### §7.1 Cl的四公理的差合化重寫" }, { "kind": "shared_concept", "use_quote": "5. **閉合性理論(DCO/Cl)**: Closure的四公理", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000477", "to": "lm-000095", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "但在本文框架下，MDAS 需要升級為：\n\n> 世界束展開後的概念—因果—狀態管理系統。", "concept": "MDAS-TCH" }, { "kind": "shared_concept", "use_quote": "但在本文框架下，MDAS 需要升級為：\n\n> 世界束展開後的概念—因果—狀態管理系統。", "def_quote": "MDAS三態因果超圖論 v2.0：認知-計算解耦架構與態空間的量子擴展", "concept": "MDAS-TCH" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000477", "to": "lm-000096", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "但在本文框架下，MDAS 需要升級為：\n\n> 世界束展開後的概念—因果—狀態管理系統。", "concept": "MDAS-TCH" }, { "kind": "shared_concept", "use_quote": "但在本文框架下，MDAS 需要升級為：\n\n> 世界束展開後的概念—因果—狀態管理系統。", "def_quote": "本文建立MDAS三態因果超圖論（MDAS-TCH）——一個將任何理論體系轉化為可計算、可視化的量子拓撲網絡的數學框架。", "concept": "MDAS-TCH" } ], "type": "concept_dependency+extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000477", "to": "lm-000464", "weight": 0.54, "evidence": [ { "kind": "external_ref", "quote": "差合化三位一體可用來描述世界束展開的底層動力。" } ], "type": "depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000477", "to": "lm-000776", "weight": 0.5, "evidence": [ { "kind": "external_ref", "quote": "TCF 不只是理論文檔格式，而是世界束展開後的壓縮層。" }, { "kind": "shared_concept", "use_quote": "TCF 不只是理論文檔格式，而是世界束展開後的壓縮層。", "def_quote": "本文提出 **Theory Compression Format（TCF）**，一個將任意形式理論規範化為統一九節結構的標準格式。", "concept": "TCF" } ], "type": "applies+concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000567", "to": "lm-001089", "weight": 0.21, "evidence": [ { "kind": "external_ref", "quote": "**DCO / Cl** | L2 的中心奇異點" } ], "type": "uses", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "The only touchpoint is a single row in a one-line cross-reference table in §7.1 (\"DCO / Cl | L2 的中心奇異點\") that assigns DCO/Cl a one-phrase role among a dozen unrelated theories; the from-paper (about MR 2.5/3.0 notation rendering) never eng…" } }, { "from": "lm-000630", "to": "lm-000119", "weight": 0.567, "evidence": [ { "kind": "external_ref", "quote": "2024年12月，作者完成《動態速率理論2.9：認知與計算的解耦——P vs. NP問題的終極動力學解構》" }, { "kind": "external_ref", "quote": "P vs NP問題問的不是\"P等於NP嗎\"，而是：**在時間的河流中，我們能否逆流而上？**", "concept": "PvsNP" }, { "kind": "shared_concept", "use_quote": "第一項研究（動態速率理論2.9）試圖解構P vs NP問題，提出\"認知搜索-計算執行-驗證\"的三階段解耦模型", "def_quote": "動態速率理論 → P vs NP 結構連續模型 2.0", "concept": "PvsNP" } ], "type": "applies+concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000712", "to": "lm-000075", "weight": 0.765, "evidence": [ { "kind": "external_ref", "quote": "**交叉引用：EML-PHYS-2026-DEPTH-v1.0 × EML-FDRS-2026-v2.0**" }, { "kind": "shared_concept", "use_quote": "信息失真算子 $\\mathcal{D}$、表示轉換算子 $\\mathcal{R}$、維度元算子 $\\Delta$", "def_quote": "信息失真算子的設計目標是：給定任意一次結構轉換（不論是展平、模式切換或維度降解），提供一個數字化的「代價」，使不同轉換路徑的代價可以統一比較。", "concept": "InformationDistortionOperator" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000712", "to": "lm-000076", "weight": 0.5, "evidence": [ { "kind": "shared_concept", "use_quote": "信息失真算子 $\\mathcal{D}$、表示轉換算子 $\\mathcal{R}$、維度元算子 $\\Delta$", "def_quote": "### Definition 3.1: Single-step information distortion operator D(Δ₁).", "concept": "InformationDistortionOperator" }, { "kind": "shared_concept", "use_quote": "它在抽象的鏈複形範疇內建立了三個連接算子", "def_quote": "### Definition 2.4: FDRS Admissible Chain Complex (`FDRSComplex`)", "concept": "ChainComplex" } ], "type": "concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000776", "to": "lm-000049", "weight": 0.535, "evidence": [ { "kind": "external_ref", "quote": "Dynamic Circle Ontology v5.0（Neo.K 2026）以**閉合性 Closure** 為唯一概念原語。", "concept": "Closure" }, { "kind": "shared_concept", "use_quote": "Dynamic Circle Ontology v5.0（Neo.K 2026）以**閉合性 Closure** 為唯一概念原語。", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "applies+concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-000924", "to": "lm-000155", "weight": 0.5, "evidence": [ { "kind": "external_ref", "quote": "**編織論（WT v7.3）**：算子本體論在關係本體論域的展開。編織元（ℓ）是算子的關係本體論版本。" }, { "kind": "shared_concept", "use_quote": "**編織論（WT v7.3）**：關係本體論是算子本體論在關係域的展開，⋈是算子合成的對稱版本。", "def_quote": "# 編織論（Weaving Theory, WT）完整版 v8.0", "concept": "WT" } ], "type": "applies+concept_dependency", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-001060", "to": "lm-000049", "weight": 0.585, "evidence": [ { "kind": "external_ref", "quote": "「同出而異名」對應 Cl-2 對偶性。" }, { "kind": "external_ref", "quote": "三 = 張力場域（陰 + 陽 + 沖氣／虛位作為生成介質）", "concept": "ETN" }, { "kind": "shared_concept", "use_quote": "我是用老子作為一個跳板，看到 Cl 框架本來看不到的層次", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-001088", "to": "lm-000049", "weight": 0.6, "evidence": [ { "kind": "external_ref", "quote": "**所屬框架**：Dynamic Closure Ontology (DCO) / 閉合性理論" }, { "kind": "shared_concept", "use_quote": "DCO 以閉合性 Cl 為唯一原始概念，提出四項公理（Cl-1 自洽、Cl-2 對偶、Cl-3 守恆、Cl-4 生成性）", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-001088", "to": "lm-001089", "weight": 0.459, "evidence": [ { "kind": "external_ref", "quote": "DCO 以閉合性 Cl 為唯一原始概念，提出四項公理（Cl-1 自洽、Cl-2 對偶、Cl-3 守恆、Cl-4 生成性）" } ], "type": "depends_on", "verification": { "verdict": "weak", "method": "adversarial-agent-audit", "note": "lm-001088 genuinely relies on DCO's Cl-1..Cl-4 axioms throughout, and lm-001089 does restate exactly these axioms (lines 78-81) as part of its Cl≅R correspondence table, so the shared concept and direction are real. However lm-001089 is a …" } }, { "from": "lm-001089", "to": "lm-001088", "weight": 0.51, "evidence": [ { "kind": "external_ref", "quote": "Cl不是靜態對象，而是進行中的操作。Cl的身份由其完整展開過程定義，而非由其瞬時狀態定義。" } ], "type": "extends", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-001090", "to": "lm-000049", "weight": 0.5, "evidence": [ { "kind": "external_ref", "quote": "由於主要結論依賴 Cl 公理組,只要 DCO 成立,本論文的元定理就成立" }, { "kind": "shared_concept", "use_quote": "每個 Cₙ 局部閉合,滿足 Cl-1(自洽性)", "def_quote": "本文建立完整的Cl公理系統,包含四條公理(Cl-1自洽性、Cl-2對偶性、Cl-3守恆性、Cl-4生成性)和維度投影定理", "concept": "Closure" } ], "type": "concept_dependency+depends_on", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-001090", "to": "lm-001088", "weight": 0.35, "evidence": [ { "kind": "external_ref", "quote": "內域與外域不是兩個獨立操作的結果,是同一閉合動作的兩面。" } ], "type": "applies", "verification": { "verdict": "ok", "method": "adversarial-agent-audit" } }, { "from": "lm-001090", "to": 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